Theory of Semigroups and Applications. 1st ed. 2017

種類:

電子ブック

責任表示:

by Kalyan B. Sinha, Sachi Srivastava

出版情報:

Singapore : Springer Singapore : Imprint: Springer, 2017

著者名:

• Sinha, Kalyan B.
• Srivastava, Sachi.
• SpringerLink (Online service)

シリーズ名:

Texts and Readings in Mathematics ; 74

ISBN:

9789811048647 [9811048649]    

注記:

Chapter 1. Vector-valued functions -- Chapter 2. C0-semigroups -- Chapter 3. Dissipative operators and holomorphic semigroups -- Chapter 4. Perturbation and convergence of semigroups -- Chapter 5. Chernoff’s Theorem and its applications -- Chapter 6. Markov semigroups -- Chapter 7. Applications to partial differential equations -- Appendix A1. Unbounded operators -- Appendix A2. Fourier transforms -- Appendix A3. Sobolev spaces.
The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in e

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